Wireless communications systems are widely deployed to provide, for example, a broad range of voice and data-related services. Typical wireless communications systems consist of multiple-access communication networks that allow users to share common network resources. Examples of these networks are time division multiple access (“TDMA”) systems, code division multiple access (“CDMA”) systems, single carrier frequency division multiple access (“SC-FDMA”) systems, orthogonal frequency division multiple access (“OFDMA”) systems, or other like systems. An OFDMA system is supported by various technology standards such as evolved universal terrestrial radio access (“E-UTRA”), Wi-Fi, worldwide interoperability for microwave access (“WiMAX”), ultra mobile broadband (“UMB”), and other similar systems. Further, the implementations of these systems are described by specifications developed by various standards bodies such as the third generation partnership project (“3GPP”) and 3GPP2.
As wireless communication systems evolve, more advanced network equipment is introduced that provide improved features, functionality and performance. Such advanced network equipment may also be referred to as long-term evolution (“LTE”) equipment or long-term evolution advanced (“LTE-A”) equipment. LTE builds on the success of high-speed packet access (“HSPA”) with higher average and peak data throughput rates, lower latency and a better user experience, especially in high-demand geographic areas. LTE accomplishes this higher performance with the use of broader spectrum bandwidth, OFDMA and SC-FDMA air interfaces, and advanced antenna methods.
Communications between user equipment and base stations may be established using single-input, single-output systems (“SISO”), where only one antenna is used for both the receiver and transmitter; single-input, multiple-output systems (“SIMO”), where multiple antennas are used at the receiver and only one antenna is used at the transmitter; and multiple-input, multiple-output systems (“MIMO”), where multiple antennas are used at the receiver and transmitter. Compared to a SISO system, SIMO may provide increased coverage while MIMO systems may provide increased spectral efficiency and higher data throughput if the multiple transmit antennas, multiple receive antennas or both are utilized.
In these wireless communication systems, signal detection and estimation in noise is pervasive. Sampling theorems provide the ability to convert continuous-time signals to discrete-time signals to allow for the efficient and effective implementation of signal detection and estimation algorithms. A well-known sampling theorem is often referred to as the Shannon theorem and provides a necessary condition on frequency bandwidth to allow for an exact recovery of an arbitrary signal. The necessary condition is that the signal must be sampled at a minimum of twice its maximum frequency, which is also defined as the Nyquist rate. Nyquist rate sampling has the drawback of requiring expensive, high-quality components requiring substantial power and cost to support sampling at large frequencies. Further, Nyquist-rate sampling is a function of the maximum frequency of the signal and does not require knowledge of any other properties of the signal.
To avoid some of these difficulties, compressive sampling provides a new framework for signal sensing and compression where a special property of the input signal, sparseness, is exploited to reduce the number of values needed to reliably represent a signal without loss of desired information.
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